Our method is related to the idea of the topological charge pumping, where a momentum is replaced by an external parameter; by sweeping the parameter one obtains topological properties of the original Hamiltonian [1]}, [2]}, [3]}. Our method, however, is crucially different from charge pumping in that we replace a momentum \(p_y\)  by a physical real coordinate \(-y\) , and in this way we succeed in recovering the full dynamics in all dimensions, whereas no dynamics occurs in charge pumping in the direction replaced by an external parameter.
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